stock here: I prefer to create the news, the statistics. Often no time to do so. But I saw this lie. And did the math.
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Given assumptions
- Prevalence of Hep B in pregnant women:
0.3%=0.0030.3\% = 0.0030.3%=0.003 of the population - False-negative rate of the test:
0.2%=0.0020.2\% = 0.0020.2%=0.002
What we are calculating
You are asking for the fraction of the total pregnant population who:
- Actually have Hep B, and
- Receive a false-negative test result
That is simply: Prevalence×False-negative rate\text{Prevalence} \times \text{False-negative rate}Prevalence×False-negative rate
Calculation
0.003×0.002=0.0000060.003 \times 0.002 = 0.0000060.003×0.002=0.000006
Result
- 0.000006 of the total pregnant population
- As a percentage: 0.0006%0.0006\%0.0006%
- As a ratio: 6 per 1,000,000 pregnancies6 \text{ per 1,000,000 pregnancies}6 per 1,000,000 pregnancies (≈ 1 in 166,667 pregnancies)
Interpretation
Under your stated assumptions:
- For every 1 million pregnant women, about 6 would:
- Truly have hepatitis B and
- Be missed due to a false-negative screening result
Important clarification
This number reflects test-performance risk only, assuming:
- One screening test
- No repeat testing later in pregnancy
- No new infection acquired after testing
- Proper lab handling and reporting
In real-world public health, additional cases can arise from:
- Infection acquired after early pregnancy screening
- Documentation or reporting failures
- Missed testing entirely (not a false negative, but a systems failure)
But purely mathematically, your conclusion is correct given the stated premises.